Dark tracking, hybrid method, Conical Diffraction Microscopy, and dark addressing

ABSTRACT

A super resolution technique, intended mainly for fluorescence microscopy, acquires the three-dimensional position of an emitter, through a hybrid method, including a number of steps. 
     In a first step the two-dimensional position of an emitter is acquired, using a technique, named in this application as an Abbe&#39;s loophole technique. In this technique a doughnut, or a combination of distributions, having a zero intensity at the combined center of the distributions, is projected onto the sample containing the emitter, under conditions wherein the doughnut null is moved towards the emitter to reach a position in which the emitter does not emit light. 
     In a second step, an axial measurement is obtained using a 3D shaping method, characterized by the fact that the emitted light is shaped by an additional optical module creating a shape of the light emitted by the emitter, this shape being dependent of the axial position and means to retrieve the axial position from the shape.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/942,559, filed 2 Dec. 2019, titled “EfficientThree-Dimensional Superresolution Positioning Method,” the entirecontents of which are hereby incorporated by reference herein, for allpurposes.

TECHNICAL FIELD

The present invention relates primarily to methods and apparatus foroptical measurement, quantification and classification of biologicalobjects using markers based on an inelastic interaction between theincident beam and the marker, such as, for example, fluorescent markers,including also other inelastic interaction, as Raman or multiphotonfluorescence. In this invention, referring to fluorescence orfluorophores, has to be understood as a simplification, for concisionand clarity, for inelastic interactions. Embodiments of the presentinvention can also be applied to methods and apparatus for opticalmeasurement, quantification and classification of non-stained biologicalobjects. Embodiments of the present invention can also be applied tomethods and apparatus for optical measurement, quantification andclassification of non-biological objects as for example, but not limitedto, semiconductors.

Introduction

The present invention relates primarily to a method and a measuringdevice. It finds applications in particular in microscopy, for examplein the field of biology and the acquisition of biological informationfrom optical observation.

We use the term “biological” to describe any biological entity in lifesciences, regardless of its origin, eukaryote organisms, prokaryotesorganisms, or virus and of the purpose of the observation, be it forresearch, diagnostic or therapeutic applications. This term includes themedical, human, animal, vegetal, virus or bacteria uses of the methodand devices described.

A Microscope is an optical instrument generally used to view, analyze,or measure objects too small for the naked eye. Microscopy is used inthe field of biology, for example, to observe, study and measurebiological entities (objects) and their dynamics.

Definitions

As used this description and in any appended claims, the following termswill have the following specified meanings, unless the context requiresotherwise:

A “set” includes at least one member.

In incoherent light, a “minimum” intensity includes an instance whereinthe intensity is zero.

We refer to “lateral” to describe the plane perpendicular ornon-parallel to the chief ray of an optical system, represented in thegeometrical Optics paradigm and to “axial” for the direction ofpropagation, i.e. the chief ray in the geometrical formalism of Optics.

We refer to an “object”, in imaging context, as the luminousdistribution created by light impinging on a physical object. We assume,for simplicity sake, that this luminous object is a faithfulrepresentation of the physical object, even if we apply the samerestrictions on the concordance between the physical object and theluminous distribution created introduced, for example, in 2010 by theinventor, (Sirat 2016), hereinafter, “Sirat 2016”. We refer to the“object plane” as the physical plane in which the object is positioned.For a two-dimensional object, in this case, we assume that theMicroscope is focused on the object plane; for a three-dimensionalobject, we refer to the plane at which the microscope is focused as theobject plane, assuming that the operator had chosen, manually orautomatically, a “best focus” in agreement with some adequate criterion.We refer to “imaging plane” for any (conjugated) plane which themicroscope images, with adequate magnification, on the object positionedat the object plane, and, the “entrance plane” as the first—assuming thelight is propagating backward from the laser through the microscope ontothe object—intermediate plane. The entrance plane is imaging plane whichis the closest to the laser.

The term “value” as used herein and in any appended claims shall referto a real number characterizing a quantity associated with a parameter.It is to be understood that, in a practical context, the quantityassociated with a parameter may be characterized within some range,constituting the accuracy of a measurement. In that case, the term“value” may be used as shorthand for a distribution of values.

The term “system ruler” is used as a quantitative value describing acharacteristic scale of the system. In this invention we use, both forstandard imaging and super-resolution systems, the diffractionlimits—lateral and axial—as the system ruler. A value will be small andin many cases neglected, if it is “much smaller” than the System Ruler,where “much smaller” is defined as smaller by a factor of 3 or by afactor of ten or more, depending on the context.

The “temporality” is defined as the temporal properties. We refer tosimultaneous to events occurring at the same time, and to“quasi-simultaneous” to describe a time regime in which several eventsare recorded at a high rate such that the measurements acquired willdiffer only marginally from the measurements which will have beenacquired in a fully simultaneous measurement of the same events. In thisinvention, for concision and clarity, simultaneous will refer to bothfully simultaneous events and quasi-simultaneous events.

The “Cartesian” axes carry their well-known meaning. A three-dimensionalposition of a point or an object can be decomposed in the measurement ofthe position along each one of any three orthogonal axes. As usual inOptics, we separate between the axis along the chief ray, in thegeometrical optical formalism, referred to as z-axis or axial direction,and the two axes perpendicular to the chief ray, in the geometricaloptical formalism, referred to as x and y axes, or lateral axes.

The “dimensionality” is defined as any one of the three physical orspatial properties of length, area, and volume. In geometry, a point issaid to have zero dimension; a figure having only length, such as aline, has one dimension; a plane or surface, two dimensions; and afigure having volume, three dimensions.

The “dimensionality” of a geometrical feature shall refer to thedimensionality, of a corresponding idealized feature in the limit inwhich the size of the geometrical feature (such as the ‘diameter’ of apoint object, or the ‘width’ of a line or the ‘thickness’ of a coating)is much smaller than the size in any other dimension and tends to bezero.

A “point” is a geometrical feature in two or three dimensions with zerodimensionality and zero size. It is an overstated simplification,erasing much information on real objects, but simplifying tremendouslythe assumptions and calculations.

We refer to an object with small but not negligible sizes, compared tothe System ruler, in two-dimensions or in all the three dimensions,without distinguishing between the two cases—as “point-object”. Theterms small or negligible has to be appreciated compared with the systemruler. A point object is determined by its position and its size, whichcan be isotropic, or not, in two- or three-dimensions. But—and itdifferentiate it from a point—a point-object may consists of astructure, smaller than the diffraction limit, which characteristics maybe of paramount importance. In many cases, this structure can beapproximated by a geometrical model, and the information to be retrievedare the model's parameters. Most biological objects are, in diffractionlimited or super-resolved optical systems, point-objects, and the apriori dismissal of the information carried by the point-object and itsrepresentation as a point is a tremendous loss. The differentiationbetween points and point-objects is of major importance in thisinvention, following a previous invention by the same inventor, {Shut,2017 #12}, incorporated herein by reference in its entirety.

A “line” (and similarly other terms that refer to shapes that areone-dimensional in theory . . . ) shall refer to a geometrical feature(i.e., to a physical object, having a length, width and thickness),where the length is at least 5 times either the width or the thickness.A line object is defined following the same rationale as a point object.

A “line object” is mutatis mutandis, the lower dimensionality analog ofthe point-object,

We refer to the “center” of a light distribution, or of a sequence orsuperposition of light distributions, mainly in conjunction to putting,at this position, a null intensity or an intensity much lower than themaximal intensity; the center as to be understood in a looseconnotation, including any position close enough to the geometricalcenter of the distribution

The usual definitions are used for: “optical diffraction limit”,Rayleigh criterion, Airy disk and its radius and diameter. We use in thecontext of the invention, the terms of “super-resolution”,“super-resolved”, “super-resolution imaging” and “super-resolutionmicroscopy” (with or without hyphen) to describe optical dataacquisition, optical imaging and microscopy at a resolution higher thanthe optical diffraction limit. In imaging systems, the “Rayleighcriterion” is the generally accepted criterion for the minimumresolvable detail, even if the observed FWHM of a point or a line is, inmany cases, used as a practical evaluation of the “diffraction limit”, aqualitative term used commonly to quantify the minimum resolvabledetail.

We use the shorthand term, “diffraction size in the entrance(intermediate) plane” to characterize, in the optical system thegeometrical extent of the diffraction limit in an entrance orintermediate imaging plane. For a pixelated DMD or SLM, used for examplein image projection, the normal system will use a pixel size of theorder of the diffraction size in the entrance plane, because anyadditional resolution will be blurred by the diffraction phenomena. Wewill present a different strategy in this invention.

The “Abbe's resolution limit” as used herein is as found in(Schermelleh, Heintzmann et al. 2010), hereinafter “Schermelleh 2010”,incorporated herein by reference:

Abbe's famous resolution limit is so attractive because it simplydepends on the maximal relative angle between different waves leavingthe object and being captured by the objective lens to be sent to theimage. It describes the smallest level of detail that can possibly beimaged with this PSF “brush”. No periodic object detail smaller thanthis shortest wavelength can possibly be transferred to the image.

The expression “above the Abbe's limit” is defined to refer to an objectcontaining periodic structures containing details smaller than anydetails of the system ruler, thus limited by the Abbe's limit. Therationale of this definition is that such an object contains spatialfrequencies above the Abbe's circle of frequencies in the apertureplane.

In estimation theory and statistics, the “Cramér-Rao bound (CRB)” or,equivalently, the “Cramér-Rao lower bound (CRLB)”, expresses a lowerbound on the variance of estimators of a deterministic (fixed, thoughunknown) parameter. The precise definition employed herein is asprovided in Wikipediahttps://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound, as accessedNov. 30, 2020, which is incorporated herein by reference.

A “localized” light distribution, as the term is used herein, shallrefer to a light distribution with energies concentrated on a smalldomain. A light distribution will be localized if the energies, outsidea radius of 3.5*the half Rayleigh criteria are below 2.5% of the overallenergy.

This invention description assumes that the optical system described isclose to being “photon noise (or shot noise) limited”, as described inWikipedia https://en.wikipedia.org/wiki/Shot_noise, or is close to beingphoton noise limited, i.e. the Gaussian noise component is smaller thanthe equivalent of half the photon (or shot) noise. The optimal case isindeed a “photon noise limited” optical system as described and a“Gaussian noise limited” system will collect only part of the advantagesof this invention but is still in the scope of this invention.

“Full width at half maximum” (FWHM) is an expression of the extent of afunction given by the difference between the two extreme values of theindependent variable at which the dependent variable is equal to half ofits maximum value, from Wikipedia,https://en.wikipedia.org/wiki/Full_width_at_half_maximum, as accessedNov. 30, 2020.

We refer to the usual definition of “Telecentricity” as presented, forexample, in Wikipedia, https://en.wikipedia.org/wiki/Telecentric_lens,as accessed Nov. 30, 2020, and we distinguish telecentricities relatedto entrance pupil and exit pupil properties telecentricities asexplained there.

The usual definitions are used for “fluorescence”https://en.wikipedia.org/wiki/Fluorescence, as accessed Nov. 30, 2020,and for “fluorophores” https://en.wikipedia.org/wiki/Fluorophore, asaccessed Nov. 30, 2020,

We refer to “photobleaching” as the photochemical alteration of a dye ora fluorophore molecule such that it is permanently or temporary unableto fluoresce, as an adaptation ofhttps://en.wikipedia.org/wiki/Photobleaching, as accessed Nov. 30, 2020.

We refer to “phototoxicity” as the mechanism in which, fluorescentmolecules in their excited state, tend to react with molecular oxygen toproduce free radicals that may damage subcellular components andcompromise the entire cell. A second physical mechanism, similar butslightly different, “photodamage” has also to be considered to avoiddependence of the results of the experiment on the intensity of lightprojected on the sample.

We refer to a Digital micro mirror device—DMD in short—as described inhttps://en.wikipedia.org/wiki/Digital micromirror device, as accessedNov. 30, 2020, to describe a chip which has on its surface severalthousands, tens or hundred thousand microscopic mirrors; thesemicroscopic mirrors are arranged in a rectangular array whichcorrespond, whether used in projecting an image, to the pixels in theimage to be displayed. The DMD may be used also as a component in opticsand optical processing, mostly for image projection. We refer, as ashorthand language, to the individual mirrors of a DMD as pixels. TheDMD pixels can be in an ON or an OFF mode; in the ON mode, the micromirror reflects the light in the direct path, the direct path being thedirection of light whether the pixelated DMD will have been replaced bya plain mirror, whether, in the OFF mode the micro mirror reflects thelight in the indirect path, rotated by a fixed angle to the direct path.Both beams can be used in an optical system.

We refer to Spatial Light Modulator SLM, to describe an object thatimposes a spatially varying modulation of amplitude, intensity, phase,or polarization on a beam of light.(https://en.wikipedia.org/wiki/Spatial_light_modulator, as accessed Nov.30, 2020) The SLM includes Liquid Crystal on Silicon LCOS and devicesused in LCoS Displays using ferroelectric liquid crystals (FLCoS) ornematic liquid crystals (Electrically Controlled Birefringence effect).The SLM includes also Grating light valve GLV as described inhttps://en.wikipedia.org/wiki/Grating_light_valve, as accessed Dec. 2,2020, whether all acronyms are defined in the previous reference. Werefer to the direct path in a transmissive SLM, as the path of light forwhich the pixelated SLM is replaced by a plain optical transmissiveelement, or absorbing SLM, the most common case, only one path isavailable, unlike in the DMD.

We refer to “acousto-optic deflectors” (or acousto-optic deflectionsystems), as described https://en.wikipedia.org/wiki/Acousto-optics, asaccessed Nov. 30, 2020, to describe devices able to shift angularly, orto focus, a light beam using the Acousto-optic effect, in 1D, 2D or as afocusing mechanism. Multichannel Acousto-optic deflectors, {Pape, 1992#40} are commercial product and can be used in practical systems.

We refer to “electro-optic deflectors” (or electro-optic deflectionsystems), as described inhttps://www.conoptics.com/electro-optic-deflection-systems/, as accessedNov. 30, 2020, and commercialized by the same company, to describedevices able to shift angularly, or to focus, a light beam using theElectro-optic effect, in 1D, 2D or as a focusing mechanism.Multi-channel electro-optic modulators can also be developed.

Referring to “DMD or SLM” in this invention is a shorthand language ofany device able to impose an amplitude, intensity, phase or polarizationimage—in the sense of varying distribution of the physical parameterstated, on a coherent or incoherent beam, in most case uniform,including also, for example, but not limited to, Acousto, Magneto—orElectro optic devices.

“Singular Optics”, which includes “optical vortices” as its simplestexample is today an emerging domain of optics, with theoretical as wellas practical applications. Detailed description may be found in {Nye,1974 #37; Soskin, 2001 #38} Nye, et al., both of which references areincorporated herein by reference.

A “Wavefront shaper” is a device able to modify dynamically the lightdistribution. Wavefront shaping in Microscopy had mainly use SLMpositioned at the pupil of the optical system, and have been applied tocontrolling multiple light scattering in biological tissues, as in{Park, 2018 #41} or in {Ritsch-Marte, 2009 #39}. The same technologytools can be applied here to create simultaneously several light points,or more complex patterns.

We refer for singular distributions with radial symmetry to “doughnuts”and to the position of the zero of intensity of these distributions asthe doughnut null or in the text of {Balzarotti, 2017 #4} cited in thisinvention, as zero or center, of the doughnut.

“Inelastic optical interaction” refers to interactions between light andmatter creating photons which differ in wavelength from the incomingbeam. Inelastic optical interaction includes, but are not limited tofluorescence, multiphoton interactions, and Raman scattering.

The “locus of a singular distribution” is the ensemble of Cartesianpositions on which the intensity of the singular distribution is zero.The locus of a singular distribution defines a family of elementaryshapes, which, with adequate parameters, the “nominal parameters” andpositioned at the right position; the “nominal position” will not emit(or reflect or scatter) light. In this case we will coin the new conceptand express that the “singular light distribution embeds the geometricalshape”.

“Conical refraction” is an optical phenomenon predicted by Hamilton,(Hamilton 1831), and experimentally confirmed two months later by Lloyd,(Lloyd 1883). Both of the foregoing references are incorporated hereinby reference. Conical refraction describes the propagation of a lightbeam in the direction of the optical axis of a biaxial crystal. Hamiltonpredicted that the light emerges in the form of a hollow cone of rays.Conical refraction is an important milestone in the history of scienceand has played a role in the demonstration of the theory ofelectromagnetic waves.

However, a discrepancy between Hamilton theory and Lloyd's preliminaryexperiments and more accurate measurements and observations was pointedout by Poggendorff, as early as 1898. This unexplained results puzzledscientists for more than 150 years and prevented the use of thispowerful effect in practical systems.

A full theoretical analysis was provided by Sir Michael Berry, in Berry,(Berry 2004), which is incorporated herein by reference. Berry's alsochanged the name of the physical effect from “conical refraction” usedby Sir Hamilton, to “conical diffraction” and we will use conicaldiffraction in this invention.

Berry's paper, and the availability of synthetic biaxial crystals, athigh quality and reasonable price, paved the way to the use of conicaldiffraction as one of the most powerful tool in the optical engineeringtoolbox.

The inventor has been one of the leading scholars to understand thepractical potency of this effect. He introduced the thin crystalconcept, trading “all the beauty and elegance of Poggendorff rings andconical diffraction that you (Sir Michael Berry) developed for a dullbut efficient controllable beam shaping unit”

A prior art system based on conical diffraction for super resolutionmicroscopy is described in {Caron, 2014 #33; Sirat, 2016 #36} andincorporated here by reference.

In the present Description, the term “energy law” is defined as follows:Assuming that an object has been modeled as a mathematical abstraction,the geometrical shape, the “energy law” is the parametric relationbetween the energy, as a function of the shape parameters and theposition. It creates a relationship quantifying the energy dependence ofthe parametric space. The energy law may include the energydistribution, emitted by a luminous object with a shape identical to thegeometric shape.

In this invention, we assume in this description that the opticalsingular distributions can be controlled, in a way to switch from onetype of distribution to another, from a predetermined family ofdistributions, and to modify the parameters of the optical singulardistributions using external means, as described by Sirat in (Sirat2016). Other solutions exist, not requiring the optical singulardistributions to be controlled, and are indeed part of this invention,but they may be much more cumbersome, in the inventor opinion.

The “control means” will refer to a set of control hardware, able tomodify the inputs and a “control algorithm”, able to foresee next stepsof input values required to quantify directly or by successiveapproximations the “energy law” in a way adequate for retrieving theparameters with precision. The “inverse energy law” is a recipe, optimalor not, able to retrieve the parameters of the position and/or theshape, from a set of measurements of a single singular distribution orof a set of singular distributions. It is embedded in the controlalgorithm. It will be chosen to optimize the functional parameters ofthe system, either the number of steps required, the overall energy—orpower—impinging on the biological object, the speed of measurement, anycombination of the above or any other functional parameters of thesystem.

Even in the simplest case of a single point, the energy law is dependentof the three Cartesian positions of the point. Some choices ofilluminations, described below, in some domain, allow to decorrelate thedependence of the inverse energy law from two of the Cartesianpositions, simplifying greatly the gathering of the information andimproving the precision.

Additionally, many inverse energy laws are quadratic and loose theinformation of the sign of the position. A solution is proposed in thefollowing.

Finally, the inverse energy law is based on some hypothesis, as forexample that the object is a point, a line or a rod. Additionalmeasurements, redundant and over-determined, can be used as a validationof the hypothesis.

For purposes of the present Description, it is assumed that a separatemechanism had been used to gather the nominal position of the object.Within the scope of the present invention, this mechanism may use anymicroscopy, as widefield, confocal or super-resolution technique, or anylocalization technique, such as PALM, STED, STORM, or from a-prioriindependent knowledge.

In the context of singular distributions, a “value close to zero” shallrefer to energy used to qualitatively describe intensity projected orenergy emitted which are much smaller than the maximum intensityavailable on the projected light or of the energy emitted if the maximumof the projected light is impinging on this point. A quantitative valuefor a close to zero intensity or energy is a factor of nine between theintensity projected and the maximum intensity of the distribution orbetween the energy emitted and the energy emitted if illuminated atmaximum intensity. It is worth mentioning, that assuming Poisson noise,energy close to zero will have a noise value markedly smaller, abovethree times less, then at maximum energy. Likewise, a geometricalparameter value of shape, close to zero will have a value smaller thanone third of the full range of the parameter.

“Conical Diffraction Microscopy” or “CODIM”, refers to Conicaldiffraction Microscopy as described in {Sirat, 2016 #11} and {Caron,2014 #33}

Prior Art: Microscopy

Referring now to FIG. 1, which shows an illustration of the paradigm ofMicroscopy, 100, in the field of Biology.

Microscopy comprises the illumination, by a light source, not shown,using a microscope, 10, of a biological sample, 11, and thetime-dependent measurement, using either visual observation or adetection module 12, of the light emitted by the sample.

The sample in Biology comprises a single—or a plurality—of differentbiological entities, 13 and 14, positioned at different positions.Examples of such objects are, among others, a cell, a virus, a protein,and a DNA fragment.

Fluorescence Microscopy

Fluorescence microscopy is one of the variants of microscopy, it hasreplaced in many biological applications, the other microscopytechniques. A fluorescence microscope is an optical microscope used tostudy properties of organic or inorganic substances using the phenomenaof fluorescence instead of, or in addition to other modalities such asreflection and absorption.

In fluorescence microscopy, the sample is illuminated by light ofwavelength, or specific wavelengths, which is absorbed by thefluorophore, thereby inducing the emission of light at different,higher, wavelengths.

The illumination light is separated from the emitted fluorescence, whichis in most cases at higher wavelengths, by the use of a spectralemission filter, reducing markedly the background of the acquiredimages.

Even if fluorescence microscopy is the most common modality of its kind,many other microscope modalities, using an inelastic interaction, i.e.the sample, or an entity bounded to the sample, emitting light at adifferent wavelength than the light source, exist.

In this invention, whether we refer to fluorescent microscopy forreadability and simplicity, the other inelastic interactions, includingbut not limited to Raman, two or multi-photons microscopy, are reputedpart of this invention.

We refer again to FIG. 1, describing, at this time, a fluorescencemicroscope; in fluorescence microscopy fluorophores, tiny point sources,15 to 18, based on the physical phenomenon of one photon fluorescence,are fixed at specific positions of predetermined biological objects, 13and 14; the light emitted by the fluorophores is observed instead ofobserving the light emitted by the biological objects, 13 and 14,themselves.

Fluorophores have become an important tool for the visualization ofbiological objects. The activity and the biological informationincluding details below 200 to 250 nm, the limit of diffraction, aresystematically viewed and measured using fluorescence microscopy. Thisresolution limit is derived from the Rayleigh criterion, which in thebest case, reaches 200 to 250 nm in systems designed specifically.

It has to be noted, that in fluorescence microscopy, the informationcollected and retrieved is a map of the fluorophores and not directly animage of the biological object, as pointed out by several authors,including Sirat-2016. The relation between the measurement and theobject relies on hypothesis, which can, in most cases, be trustworthy.

The main implementations of fluorescence microscopy, as described indetail in the literature, are the confocal microscope, often used in ascanning configuration or spinning disc microscope, and the wide-fieldimaging microscope.

Referring now to FIG. 2 which is a simplified representation of aconfocal fluorescence microscope of the prior art 200. A confocalfluorescence microscope, FIG. 2 is an optical instrument. Its mainhardware components are shown in FIG. 2. They include:

a light source, 20,an optomechanical frame not showna cube filter, 21,a microscope objective 22, and,a detector assembly, 23,a processing unit, not shown.

The light source 20, which may be an arc lamp or a laser, creates lightenergy necessary for fluorescence. The Optomechanical frame, not shown,is the support of all the optical components and auxiliary optics andincludes alignment capacities. It also includes optical elements, notshown, capable of shaping the beam to allow its focus point of a minimumsize by means of the microscope objective. It can also comprise, in aconfocal scanning fluorescence, a spatial or angular scanning mechanism,not shown, to change the position of the point source with respect tothe object to be measured.

The scanning mechanism can alternatively:

-   -   mechanically translate the object, for example by using a        translation plate,    -   optically scan the beam on the object, for example using a set        of galvanometric mirrors or acousto-optic translators, or    -   use any combination of these translation means, mechanical or        optical.

In a confocal scanning fluorescence, the information is collected pointby point, using the scanning mechanism. It can also comprise, in arotating disk type confocal fluorescence, a rotating disc having aplurality of pinholes, allowing the simultaneous projection of aplurality of points. In a confocal fluorescence rotating disk, a set ofpoints, corresponding to the pinhole is acquired at any time and therotation of the disk allows to scan the entire surface of the sample fora given longitudinal position.

The cube of filters, 21, channels the different optical signals andavoids contamination of the fluorescence signal by the emission. Thecube is composed of filters: excitation filter, 210 dichroic mirror,211, and emission filter 212. The filters and the dichroic mirror areselected according to the wavelength of excitation and emission spectralcharacteristics of the fluorophore.

The microscope objective 22 focuses the light created by the source inthe focal plane of the lens 24, a light distribution pattern of smallsize, the optimum light distribution consisting of the Airy disk. Themicroscope objective 22, also collects back fluorescent light emitted bythe fluorophores.

For a confocal scanning fluorescence, the system can be descanned, thatis to say, the return light can pass through the scanning mechanism tocompensate for the translation due to scanning.

A detector lens, 25, creates, in the image plane of the detector 26, amagnified image of the focal plane of the lens 24.

A confocal hole, 27, is theoretically placed in the image plane of thedetector 26. In most practical systems, the confocal hole, 27, is placedin an intermediate imaging plane, not shown, and reimaged onto the imageplane of the detector 26.

The assembly of the detector, 23, detects the fluorescent intensity inthe overall illuminated volume, and converts it into digital signal. Inthe simplest implementation, for a confocal scanning microscope, thedetector assembly comprises a detector of a single element, such as aPhotoMultiplier Tube PMT or Single Photon Avalanche Diode SPAD. For aconfocal microscope using a rotary disc, the detector assembly iscomprised of a matrix of detector elements, such as a Charged CoupledDevice CCD, an Electron Multiplying CCD EMCCD, a common Metal OxydeSemiconductor CMOS or a matrix of SPAD.

All components mounted from the light source to the dichroic filter isthe illumination path, 201. The detection channel, 202, represents allthe components mounted from the dichroic filter to the assembly of thedetector.

Fluorescence microscopes are available from several manufacturers, suchas Zeiss, Leica, Nikon, and Olympus. Fluorescence microscopes can beeither standard microscopes suitable for fluorescence or microscopesoptimized specifically for fluorescence. Modern microscopes areversatile instruments capable of operating in many different modalities,including, but not limited to, fluorescence modalities, using the sameplatform and most optomechanical components. Most fluorescencemicroscopes are developed as an open platform, capable of performingseveral additional features with minimal modifications. Otherfluorescence microscopes are instruments dedicated, adapted for aspecific task, such as medical diagnosis or pharmaceuticals.

Prior Art: Super-Resolution

For a long time, until the emergence of super resolution techniquesdescribed below, it was widely assumed that optical techniques,including fluorescence microscopy, are unable to visualize detailssmaller than the Rayleigh criterion, which is about 200-250 nm, forvisible light.

However, other fundamental biological activities also occur at scalessmaller than 200 nm in biological samples. At this level of spatialresolution, important phenomena can be observed: the biologicalprocesses at the scale of intracellular, cell information transfer, thefolding and unfolding of the proteins and changes in the DNA and RNA.For example, the measurement of this intracellular information opens newavenues for understanding the biological activity, and lead to progressin understanding and monitoring of research and medical diagnostics.

“Super-resolution microscopy, in light microscopy, is a term thatgathers several techniques, which allow images to be taken with a higherresolution than the one imposed by the diffraction limit.” (contributors2019). We use the definition found in Wikipedia, for STED, localizationmicroscopy, PALM, STORM, and many other modalities, described forexample in https://en.wikipedia.org/wiki/Super-resolution_microscopy, asaccessed Nov. 30, 2020. We include also in super resolution, additionalsuper resolution modalities known to the man of Art.

Conical Diffraction Microscopy is a super resolution modality, developedby the inventor (Sirat 2016), hereinafter, “Sirat 2016”.

Several microscope modalities use a reconstruction process, i.e. thedirect data retrieved physically by the detecting system is not thefinal result and an algorithmic step is required to retrieve the finalimage.

The positivity constraint, the physical fact that light intensity isintrinsically positive, adds a supplementary restriction on themathematical solutions for optical systems in which an algorithm is usedto calculate the final object (reconstruction). The positivityconstraint can be applied on the general cases, limiting the field ofpossible solutions, and so improving someway the result quality.However, in a specific case, named by the inventor Abbe's loophole, anddescribed below, this constraint allows to overcome the Abbe's limit ofresolution, it is the case with this invention.

Imaging, Localization and Tracking

We refer, in this invention, separately to two differentfunctionalities: imaging and localization, even if, in many cases, thetwo functionalities can be assessed on the same instrument.

In imaging we are observing an object, without implying any additionalinformation, a priori, on this object. Localization assumes that theobject is a point and can be parametrizes by a small number ofdescriptors. “Tracking” is a shorthand term to dynamic localization, orlocalization as function of time, and we will use either localization ortracking, depending on context.

In imaging, the observed object, which differs from the original object,can be described, in a degrees of freedom formalism, with a finitenumber of degrees of freedom, limited by the optics system (Lukosz1966). The observed object is conceived as a filtered version of theoriginal object, and is limited by diffraction, in the general case,even if some super resolution schemes can be applied.

In localization, the object is known, or is hypothesized, to be a singlepoint; it is a parameter searching problem, which is quantified byCramér-Rao criterion and is definitely not limited by the diffractionlimit, but by the signal to noise ratio.

Between these two extremes, the total absence of a priori information,and the parametric description of the object, many cases exist, in whichsome partial information exists. As an example, the assumption that thescene consists of sparse objects allows some additional information onthe object, which, in some cases, can be translated to additionalinformation or resolution. In (Sirat 2017), for Abbe's loopholetechniques described below, the inventor extended the localizationproblem of a single emitter to the case of a simple geometrical objectretrieving both the position and the geometrical descriptors.

And Metrology

We refer to “Metrology” as a third modality, besides imaging andtracking, as a modality in which we acquire, besides the position of asingle point, or a small set of single points, a set of descriptivegeometrical parameters, describing the observed entities as simplifiedgeometrical—or/and temporal—objects, as described in in (Sirat 2017)incorporated here in its entity. The inventor considers Metrology as a,new, additional modality of this invention, with practical impact asvaluable as imaging and tracking.

Localization Alternate Paths

Globally, two strategies, which can be applied either for lateral oraxial measurements, or conjointly for both, exist to determine theposition of an object, assumed to be an emitting point of infinitelysmall size (refers below in short as an emitter), above the limit ofdiffraction:

-   -   Projection strategy: Projecting a light distribution with        infinitely small size and recording the returned energy    -   Emission strategy: analyzing the returning light, under the        assumption of an infinitely small size

The STED modality, described inhttps://en.wikipedia.org/wiki/STED_microscopy, as accessed Nov. 30,2020, and in the cited references there, is the archetype of theProjection strategy of localization. By careful nonlinear engineering,the projected light is concentrated to a size smaller than thediffraction spot, theoretically unlimited, in the case of the projectionof infinite energy. Both two-dimensional and three-dimensional solutionsare described and implemented in real working systems.

The localization techniques, described inhttps://en.wikipedia.org/wiki/Super-resolution_microscopy#Localization_microscopy_SPDM,as accessed Nov. 30, 2020, including techniques named PALM and STORM arethe archetype of the Emission strategy of localization. Assuming theemitter is a single point, the spot centroid, for two-dimensionallocalization, if the light distribution created on a detector is asingle spot, can be retrieved through adequate algorithms; it is ameasure of the position of the emitter. The position can be retrievedwith infinite precision, assuming infinite energy.

More evolved techniques, mostly devoted to three-dimensionallocalization, shapes the emitted light, using adequate optical means, as(Pavani, Thompson et al. 2009) or (Fallet, Dubois et al. 2015) asexamples, creates a more complex, and more accurate, relationshipbetween the localization values and parameters of the shape of the lightdetected. We refer in this invention to these techniques asthree-dimensional shaping of the emitted light. These techniques areable to measure the axial position of an emitter but require a minimalnumber of photons to do so.

We refer in this invention to “3D projected light shaping methods” tomethods, characterized by the fact that the light projected by theemitter is shaped creating a predetermined shape, this shape beingdependent of the axial position and means to retrieve the axial positionfrom the shape. The concept of the 3D STED is one example of suchmethods: in CODIM, {Fallet, 2015 #15; Fallet, 2016 #35; Sirat, 2016 #11;Sirat, 2017 #8; Sirat, 2017 #12; Sirat, 2017 #31; Sirat, 2016 #36;Sirat, 2017 #34} describe several means to shape the projected light tomake it axially dependent.

We refer in this invention to “3D emitting light shaping methods” tomethods, characterized by the fact that the light emitted by the emitteris shaped by an additional optical module creating a predeterminedshape, this shape being dependent of the axial position and means toretrieve the axial position from the shape. A review of some of thesetechniques can also be found in (Martens, Jabermoradi et al. 2020).

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention will be more readily understoodby reference to the following detailed description, taken with referenceto the accompanying drawings, in which:

FIGS. 1 and 2 reproduced from Sirat-2016 are simplified representationsof a fluorescence.

FIG. 3 represents the different singular distributions available usingconical diffraction for projected light.

FIG. 4 represents four alternatives to create a single point from anincoming beam of light, assumed, but not required, to be a parallel beamat the entrance of the device. FIG. 4A describes the use ofgalvanometric mirrors, assumed, as it is common in confocal system to bea pair of orthogonal controlled mirrors; FIG. 4B describes the use of anacousto-optic deflector, FIG. 4C describes the use of a SLM or a DMD,FIG. 4D describes a different use of a SLM or a DMD, and FIG. 4Edescribes another different use of a SLM or a DMD.

FIG. 5 describes a simplified algorithm and process to retrieve the two-or three-dimensional position of an emitter. FIG. 5A and FIG. 5B,represents horizontal and vertical symmetrical patterns of lightdistributions, and FIG. 5G to FIG. 5J, represents horizontal andvertical asymmetrical patterns of light distributions; the position ofthe emitter is materialized by a star on these Figures; FIGS. 5C-5Erepresents an axial dependent pattern, of light distributions, describedin {Shut, 2016 #11}; FIGS. 5C-5E represent 3 cuts of the lightdistributions, at different axial positions, represented as FIG. 5C,FIG. 5D and FIG. 5E, namely, (1) at focus, (2) at an axial position of0.1 Rayleigh range, and (3) at an axial position of 0.2 Rayleigh range.FIG. 5F, describes the relative geometry of the distributions and theemitter.

SUMMARY OF EMBODIMENTS

In one embodiment, the present invention provides a method fordetermining a position in three dimensions of a light-emitting object ina sample. In this embodiment, the method includes:

-   -   characterizing two of the dimensions of the position in a first        coordinate system using an Abbe's loophole technique, by        projecting along a first projection axis, onto a part of the        sample including the light-emitting object, a first set of        distributions of optical radiation having zero intensity at a        common center of each of the distributions of the set, measuring        the intensity of the light emitted and moving the set of        distributions to a first location on the object wherein the        light emissions are at a minimum, such location characterizing        such two of the dimensions; and    -   using an optical module to shape the light emitted from the        object, before detecting the light, in a manner wherein a        resulting shape depends on an axial position of the object,        recording the shape and the overall intensity, and using the        resulting shape measurement to determine the axial position.

In a related embodiment, the invention further includes determining theposition of the light-emitting object, with even higher accuracy, bycharacterizing all three of the dimensions of the position in a secondcoordinate system using the Abbe's loophole technique, by projectingalong a second projection axis onto the object a second set ofdistributions of optical radiation having zero intensity at thethree-dimensional position of each of the distributions of the set,determined according to claim 1, and moving the set of distributions toa second location on the object wherein the light emissions are at aminimum, such second location characterizing all three dimensions.Optionally, the method further includes, before characterizing two ofthe dimensions of the position in the first coordinate system, acquiringa rough estimation of the position of two- or three-dimensional positionof the light-emitting object, by standard localization or imagingmethods. In a further related embodiment, the invention furtherincludes, in the course of projecting a set distributions selected fromthe group consisting of the first set and second set of distributionsand combinations thereof, onto the light-emitting object, measuring theintensity of light emitted along a selected Cartesian axis in adelimited region thereof including a location having minimum intensity,wherein such intensity along such Cartesian axis yields a measure of theposition of the light-emitting object along such Cartesian axis,decorrelated from position of the light-emitting object along otheraxes. In a further related embodiment, the set of distributions includesat least two distributions. In a further related embodiment, the set ofdistributions of optical radiation having zero intensity at a commoncenter of each of the distributions of the set, is chosen such that theset of values measured from the intensities and shapes is selected fromthe group consisting of redundant and over determined, in order toprovide validation of the determined position.

In another embodiment, the invention provides a method for determining aposition in two or three dimensions of a set of separated light-emittingobjects. In this embodiment, the method includes characterizing two orthree of the dimensions of the position of each one of the separatedlight emitting objects, by projecting, using a scanning device, along aprojection axis, onto each object of the set of objects, a set ofdistributions of optical radiation having zero intensity at a commoncenter, in two or three dimensions, of each of the distributions of theset of distributions, the center being different for each object of theset of objects, measuring the intensity of the light emitted and movingthe center of set of distributions, by using a scanning device,separately for each object of the set of objects, to a location on theobject of the set of objects, wherein the light emissions are at aminimum. Optionally, the scanning device used to move the positions ofthe is a SLM or a DMD, positioned at a plane conjugate to the sample,and the scanning device is operating, for a SLM or a DMD, in a mode thateither only pixels conjugated to the position of the determinedpositions are in ON mode and the light collected is the direct path, or,alternatively, in a DMD, only pixels conjugated to the position of theemitters are in OFF mode and the light collected is the indirect path.In a related embodiment, the size of the spot corresponding to thediffraction limit is larger than the pixel size, by a factor between 3and 11. In further related embodiment, an algorithm is applied todetermine an adequate combination of pixels ON and OFF, to position thecentroid of the spot on the sample with resolution better than a single,full, pixel of the scanning device, projected on the sample plane. Inyet a further related embodiment, a first optical module is used tocreate a light distribution including the emitters position as part ofthe illumination domain. Optionally, the scanning module is selectedfrom the group consisting of a multichannel acousto- or electro-opticdeflector and a Wavefront shaper, and combinations thereof.

DETAILED DESCRIPTION OF EMBODIMENTS Abbe's Loophole

We refer to Abbe's Loophole, a term coined by the inventor, in previouspatent applications and publications, to describe a family of projectiontechniques in which the localization of an emitter is derived from theabsence of light created by the projection of an optical pattern,including in an approximate center a null of energy on the emitter,assumed to be of infinitely small size.

The rationale of this formulation is that Abbe's law precludes directmeasurements of spatial frequency components above the diffractionlimit; however, the positivity constraint creates an additionalunderlying relationship between all frequency components. In thespecific case when all frequency components, below the diffraction limitand the spatial DC component are all zero (black image) this constraintrequires that all frequency components above the diffraction limit willbe also zero. In this loophole, the frequency components, both below andabove the diffraction limit are known—to be zero and this indirectmeasurement of all frequency components is a practical breach of thediffraction limit.

We use, in this invention, the nickname “white system” for describing alocalization system based on the emission strategy described above and“black system” to describe a localization system based on the Abbe'sloophole.

One family of techniques based on Abbe's loophole, uses a vortex, oranother similar distribution with a zero intensity precisely orapproximately at the center, as the light distribution projected on thesample. This technique had been proposed in (Sirat 2017), a divisionalpatent of (Sirat 2016), with priority date of October 2010, using thename of “black fluorophore”. This technique is also described in (Hell2016), with priority date of November 2011, and later in several papersas (Balzarotti, Eilers et al. 2017, Gwosch, Pape et al. 2019) publishedand commercialized under the name of MINFLUX.

The extension to a three-dimensional case, with appropriatethree-dimensional distributions, can be found in the cited references.

A different, and complementary technique, for which the inventor coinedthe name, in publications, as “dark tracking”, uses a plurality of lightdistributions, with similar radial functionality and common centralzero, but different azimuthal dependences, projected on the samplesequentially (Sirat 2016, Sirat 2017). This technique had been proposedin (Sirat 2017), a divisional patent of (Sirat 2016), with priority dateof October 2010.

The differentiation of these two techniques, lies in the acquisition, indark tracking, with the same photon count, of the azimuthal angle inaddition to the radial information, the only information available inthe “black fluorophore”/MINFLUX technique. This additional informationsimplifies much the ability to reach the position whether the zero—inthis case of the aggregate of the distributions—is positioned on theemitter.

A derived technique, referred by inventor as “Metrology” in (Sirat 2017)generalized the “dark tracking” technique to emitter consisting ofsimple geometrical objects, as point-objects and line-objects definedabove, and not on infinitely small points, in order to retrieve both theposition and geometrical descriptors of the emitter shape.

We refer in this invention to “dark addressing” to describe a techniquewhich allows to perform dark tracking simultaneously—or quasisimultaneously—on several identified targets as described in thefollowing.

These techniques allow additional resolution, theoretically unlimited,by combining

-   -   a loophole of Abbe's law    -   the almost total absence of noise, in the specific case        described as the Abbe's loophole, due to Poisson's law    -   an anomaly in Cramér-Rao bound, close to zero intensity.

To get the best performances from these techniques, the absence of anyspurious photon, is expected, in order to fulfill the theoreticalconditions and to reach the optimal, unlimited resolution. The absenceof spurious photon condition or at least its minimization, is moreeasily met using inelastic light interactions, as fluorescence,multiphoton interactions and Raman scattering; in these modalities, theincoming beam can be totally filtered by spectral means, without(almost) sparing a single photon.

All other optical techniques can also make use of these principles evenif background photons will limit the ultimate resolution achievable andare part of this invention.

To be more precise, the techniques described above as Abbe's loopholetechniques can be structured as involving three steps: a detection step,an intermediate step (to position the doughnut null or the dark trackingcombined zero, close up to several nm or below 20 nm, to the emitter,this step nicknamed “daemon step”) and a precision step.

The earliest description of what we refer to as the daemon step had beenstated in Sirat 2010. However, we follow the later description in(Balzarotti, Eilers et al. 2017), referred as Balzarotti-2017, cited inextenso, due to its didactic and self-explanatory redaction, to describethe techniques we refer to as Abbe's loophole solutions in thisinvention and their limits:

Let us now perform a gedanken experiment in which we seek to establishthe trajectory of a molecule diffusing in space. Instead of usinguniform widefield excitation and a camera, we now excite with areasonably bright focal doughnut that can be moved rapidly throughoutthe focal plane. If we, or a demon, now managed to target the zero ofthe doughnut shaped excitation beam exactly at the molecule, steering itso that it is constantly overlapped with the molecule in space, thedoughnut-targeting device would map the molecule in perfection withouteliciting a single emission. On the other hand, a single emission (e.g.due to a minimal misplacement) would be enough to know that the moleculeis not at the location of the doughnut zero.Unfortunately, we cannot know the position of the molecule in advanceand place the doughnut to that coordinate in a single shot, which is whyperfect localization without emissions will remain the privilege of thedemon. Yet, this gedanken experiment suggests that multiple shot probingof the position of a molecule with an intensity zero should reduce theemissions required for localization. This is because, in our picture,the fluorescence emissions are the price to be paid for not knowing theposition, and the closer the zero gets in the course of probing, thelower will be the price. As a matter of fact, the emissions are highlyvaluable because, apart from confirming the presence of the molecule,they convey information about its distance to the probing zero.

In this application we refer to an Abbe's loophole technique, or a blacktechnique, as a technique, using a doughnut or a combination or asequence of distributions, in two or three dimensions, specific in thefact that a zero of intensity, or an intensity close to zero, exists atthe combined center of the distributions, in one, two or threedimensions, is projected on the sample containing the emitter and thatthe doughnut null is moved towards the emitter to reach a position inwhich the emitter does not emit light.

A two-dimensional Abbe's loophole technique can use a doughnut or acombination of distributions, as the conical diffraction distributionsrepresented in FIG. 3, projected sequentially or concurrently, on thesample, whether a three-dimensional Abbe's loophole technique will add adistribution which is zero at the axial position of an emitter,

Some embodiments of the Abbe's loophole techniques include also means tocontrol the system and to modify the relative position of the null andthe emitter

In short, we are able to reach almost infinite theoretical resolution,whether the distance between the molecule and the doughnut null, is ofthe order of a few nms, with minimal photon cost; however, at thestarting point the null can be separated from the molecule by a distanceof the order of more than 100 nm. The intermediate steps nicknamed“daemon step”, which in many cases are subsequent sets of measurements,are not in the low photon regime and has to be engineered carefully.

The starting point, the detection of the presence of the emitter, andits unicity, is used in many cases and uses relatively standardtechniques; it allows reaching diffraction limit precision, (200-250nm), or with some additional developments 90-100 nm precision, asobtained by super resolution systems exemplified by the super resolutionsystems developed by the inventor, using (Sirat 2016); its photon andsystem complexity cost can be lowered by reducing the precisionrequirements, but with the obvious additional burden on the second step,the intermediate daemon step.

The last step, whether the doughnut null is positioned at the moleculeor very close to it, reach a few nms precision, is surprisingly, quitesimple on conceptual grounds. It is the step in which (theoretically) asingle photon will carry a YES/NO information.

This controversial statement, on the inherent simplicity of the laststep, is accurate only on the conceptual level. Still, the systemrequires carefully engineered optics, single photon detection, motioncontrol to the nanometer level and low noise electronics. Thesetechnical specifications are required to avoid creation of any spuriousphoton, electron, or digital count and to control motion. Nevertheless,all these requirements are in the realm of existing, well-entrenchedsystems and technologies, even if the combination of all these extremesspecifications is utterly challenging.

The really challenging step, on both conceptual and practical ground isthe intermediate (daemon) step, to bridge between the starting point of100 nm precision and the few nms of the last step, in a deterministicreliable procedure and at a reasonable photon and system complexitycost.

Another point to be noticed, which make the Abbe's Loophole techniquesintrinsically superior to other techniques, is the fact that, in manybiological situations, the point of interest will remain static, orfollowing a predictable path, for a long time. A sudden, unscheduled,event will modify the dynamic of the point of interest. These events maybe the trigger of a major incident, as for example, an apoptosis ornecrosis incident.

The cost, in photons, of the waiting time is, in Abbe's loopholetechniques theoretically zero and the waiting can last for a long time.An event will trigger a burst of photons, which will be immediatelyrecognizable, and will be the trigger for detection of the event. Allwhite techniques will require checking the position of the pointrepeatably, with a sizeable photon cost for each interrogation.

Another point to be noticed, which make the Abbe's Loophole techniquesintrinsically superior to other techniques, is the fact that, assumingthe system is well-designed and able to reach speed above the typicalspeed of movement of the particle, after the system lock on the target,using purposely a language reminiscent of antiaircraft jargon, the costin photons to track the particle can be reduced by proper observationand control.

A major issue, which will be even more important in the next paragraph,is to identify the molecule: in fluorescence, as well-known to the manskilled in art, two main mechanisms of recognition of a specificfluorophore is the emission/projection wavelengths specificities, whichlead to multiwavelength systems and the Life Time characteristics, whichmay also be a tool to differentiate fluorophores.

The measurement of the lifetime of the incoming photons is possible,whether photons are available . . . . It is of major importance in thedaemon step, and also in precise step in order to recognize if theincoming photon is created by the observed target or by a spuriousfluorescence, a ghost image, a nearby object or any other parasiticlight.

Finally, the presence of the target may require to be assessed from timeto time and the responsivity of the target to light, the amount of lightavailable for a given projected power is required by some, but not all,algorithms. The availability, in Conical Diffraction basedimplementations, of distribution similar to a gaussian beam, or an Airyshape, of controllable amplitude, is of important impact on thepracticability of real-world systems and is part of this invention.

Description of Embodiments of the Present Invention: Hybrid Solution

A new method is presented herein, in which the measurement procedure isa separate, dedicated procedure and architecture, initialized in somecases by an imaging procedure.

The invention described below is directed towards accurately localizingan emitter, with precision above the diffraction limit of light employedin their measurement, with minimal flux.

This invention is especially adapted to accurately localizing featuresusing inelastic light interaction, as, but not limited to, fluorescenceor Raman scattering, in which the emerging light can be separated bysimple means from the incoming light but can be applied as well to othermicroscopy modalities.

Methods in accordance with embodiments of the present invention mayadvantageously provide for measurement entailing resolutions greaterthan the diffraction limit imposed by the optics and minimal photonfluxes.

This method can be used as either an alternative to the Abbe's loopholethree-dimensional techniques, whether the three-dimensional requiredresolution is in the ten nanometers range or, alternatively to simplifythe “daemon step” and reduce its photon cost.

We refer to this new method as the “hybrid method”. It is describedbelow, and uses localization in two or three dimensions, based onanalysis of the emitted light, in the intermediate step in order tomeasure the position of the emitter. The hybrid method can be used fortwo-dimensional localization, but the preferred embodiment is to recordthree-dimensional position of the emitter using the photons emittedanyway.

This technique is named hybrid, because it is combining, in thepreferred embodiment, in a dedicated methodology, projection andemission strategies of localization, namely the use of projectionstrategy to acquire the two-dimensional lateral position, and emissionstrategy, through three-dimensional shaping to acquire the axialposition.

The use of a three-dimensional shaping of the emitted light, as the toolto retrieve the axial position, with a reasonable precision of the orderof 10 to 30 nms, using three-dimensional beam-shaping is a goodsolution, taking advantage of physical existing data and informationreadily available, if properly engineered. The three-dimensional shapingof the emitted light uses photons created, anyway, by thetwo-dimensional doughnut, used to retrieve the lateral position using aprojection strategy. These photons exist anyway, because the emittingpoint is still not close to the doughnut null. It reduces markedly thecost in photons and increase the speed of reaching the doughnut null.

Additionally, the three-dimensional information is the most expensive toacquire, in term of photons and system complexity. It requires thethree-dimensional equivalent to a doughnut which indeed exists but isfar less efficient then the two-dimensional doughnut, due to fundamentalprinciples. It also requires an approach of reaching thethree-dimensional position of the emitter by acquisition in thethree-dimensional space of many different positions.

In Abbe's loophole techniques, the addition of a three-dimensionalrequirement, complexify markedly the system; the demon has to be veryclever!! A change of energy can be due to a movement in any of the threecartesian directions or any combinations of them. To retrieve thedirection in space in which to move the null of the doughnut—or of anequivalent set of distributions—requires many measurements, whichtranslate to a heavy photon budget.

The aim of this invention, whether used as an intermediate step in anAbbe's loophole technique, is to avoid daemon burn-out. We simplify histask by acquiring independently an axial information, by differentmeans; the axial information retrieval is based on photons alreadycreated in the process by the projection strategy of localization usedfor the lateral dimension's localization. This independent informationis acquired using an emission strategy of localization, complementary ofthe projection strategy of localization, based on Abbe's loophole, usedfor localization of the lateral dimensions

In conclusion, this invention proposes a novel, unheard before,solution, by using a hybrid system, which consists of a specific,efficient, use of the information available, in a way not proposedbefore.

In another configuration, the invention consists of three subsequentsteps:

DETECTION STEP: In the detection step the detection of the existence ofthe emitter, its unicity and a preliminary three-dimensional position ofthe emitter is obtained. Many different techniques can be used for thedetection step, including but not limited to confocal and widefieldMicroscopy. The position may also be known from another a priori orexternal knowledge. The choice of the technique will be partiallydictated by a low photon requirement.

DAEMON STEP: Acquiring the three-dimensional position of the emitter,through the hybrid method, described in this invention,

PRECISION STEP: Acquiring the three-dimensional position of the emitter,consisting of the acquisition of the three-dimensional position usingone of the three-dimensional Abbe's loophole techniques, as described inthis invention, including moving the null of the distribution towardsthe particle, with highest possible precision of a few nms.

Description of Embodiments of the Present Invention: MultipleSynchronized Points

The previous discussion, following (Hell 2016, Sirat 2016, Balzarotti,Eilers et al. 2017), presented the concept of measurement of theposition of a single point, in one-, two or three-dimensions,potentially with several wavelengths, with high accuracy, high speed andlow photobleaching and/or phototoxicity. However, many differentbiological mechanisms rely on synchronized elementary events, and thecapacity, to acquire, SIMULTANEOUSLY (or quasi-simultaneously), severaltargets, separated optically, by a distance above the system ruler or afew system ruler, can be of major impact on the Biology and Medicalfields.

With no need to give detailed examples, many biological functionalevents are complex, and are the result of signal trafficking and onsubtle balances between several enabling and disabling signals and thedynamic of these signals is of paramount importance.

In this invention we differentiate and define, in super resolutionMicroscopy, in Microscopy in general, and generally in target highresolution following, a new paradigm: the multi-target follower scenarioand adjust it to all black systems, even if the same scenario can bealso applied to white systems and is reputed part of this invention.

The multi-target follower scenario is defined as the simultaneous—orquasi-simultaneous—measurement of a limited number of small target, aspoints, points-objects, lines, lines objects or simple geometrical smallstructures.

The additional complexity of this scenario is fully counterbalanced bythe importance, in Biology of this specific case. Both confocal andwidefield geometries are simpler indeed, easier to implement, but theperformances gap is huge, in comparison to the development effort ofthis scenario dedicated and optimized to the multiple synchronizedpoints.

The inventor state again that such a measurement system will have majorimpact of the capacity to measure, visualize and quantify the rootcauses of functional Biology activities, these root causes may be in theform of elemental molecular events; it is of paramount importance andworth developing a dedicated optimized solution.

The inventor state also that this scenario is well adapted, andcomplementary to two concepts introduced in his last invention, {Sirat,2017 #12}, referred to here in its entity, which introduced a metrologyand a deep learning schemes. The metrological features introduced thereare different information, well-suited to the goal of correlatingelemental events to functional information and the deep learningcapacity is an additional tool to extract meaningful information.

Using again the antiaircraft jargon, the multi-target follower scenariosimulates a synchronized attack of several planes and missiles, ofdifferent characteristics, speed, and lethality, whether the singletarget case concentrate on a single specific plane.

The solutions presented by (Hell 2016, Sirat 2016, Balzarotti, Eilers etal. 2017) are built on a confocal configuration, a single point (andtarget) and on a scanning system. To duplicate the point, and the pointfollowing technique, is cumbersome and will require an overly complexsystem—but not impractical unlike stated in (Gu, Li et al. 2019).

Other solutions based on widefield configurations as SIMFLUX, (Cnossen,Hinsdale et al. 2019), ModLoc, (Jouchet, Cabriel et al. 2020), SIMPLE(Reymond, Ziegler et al. 2019) and ROSE, (Gu, Li et al. 2019), lack theadvantages of Abbe's loophole techniques.

In other words, the two existing simplified conceptual geometriesdescribing the light dimensionality and dynamic projected on the object,namely confocal and widefield, are not fitted to the problem andchallenge described here, which is specifically the tracking andidentification of multiple but a small number, independent, targets. Dueto the choice of a unoptimized configuration, all previous art solutionswill require some compromise, either by giving up performances, orrequiring a huge technological cost; mainly the confocal solutions maygive up the simultaneity, whether the widefield solutions are projectinglight everywhere, polluting the signals.

To specify a new geometry of light interaction, we reconsider theelementary point formation process, FIG. 4A. Assuming a uniform beam oflight, [40], the straightforward solution to create a single point [50],is, obviously, to focus the beam using a lens or an the optical system,[43], and to use mechanical means—as galvanometric mirrors [41] and [42]to move the point, [50], on the object plane, [49]. FIG. 4A is theunderlying configuration used in a confocal system. The point positioncan be controlled using a scanning mechanism, such as a galvanometermirror, as in FIG. 4A, or using an acousto-optic deflector, FIG. 4B.

In FIG. 4B, a uniform beam of light, [40], is deflected using anacousto-optic deflector, [44], focused using a lens or an the opticalsystem, [43], to create a single point [50] on the object plane, [49].

A different solution, FIG. 4C exists: a uniform beam of light, [40], isprojected on a controllable DMD or SLM, [48], represented as areflective DMD device, even if transmission, similar, solutions exist.The DMD is positioned at the imaging plane of a lens or an the opticalsystem, [43]; assuming all the pixels are switched off, except a singleone, [46], as in FIG. 4C, or a small region which geometrical extent issmaller than the diffraction limit, consisting of a number of adjacentpixels, [47], FIG. 4D, a single point [50], will appear on the objectplane, [49]; the point position is dependent on the single pixelposition, in in FIG. 4C, or of the centroid of the region illuminated onthe DMD or SLM in in FIG. 4D. Additionally, we assume, in FIG. 4D, inthe case of a small region, that the light emerging from the pixel,reflected—or transferred, is coherent and that no additional phase delayoccur between adjacent pixels, even if other cases may be alsoconsidered with a loss of performances.

The solution described in in FIG. 4C exists but in normal conditions, isconsidered as a poor alternative, with many drawbacks, to standardsolutions, as the ones presented in in FIG. 4A and in FIG. 4B. Thereason that this solution is seldom used is that, for a single point,the energy efficiency of such a solution is tremendously low, makingsuch a solution almost unpractical. Indeed, all the light impinging onthe OFF pixels is simply lost. To put numbers, assuming that the regionscanned by the system is of 10*10 μm on the sample, and for a 250 nmdiffraction limit, the energy loss is of the order of, roughly speaking,1:1600, not taking into account additional geometrical losses.

Additionally, such a solution, if a single ON pixel is used, will allowpositioning the point at discrete positions, corresponding to fullpixels, and so will clearly not be adapted to Abbe's loophole systems,which require nms movement of the point. As explained below, the use ofa small region, smaller than the diffraction size in the entrance plane,allows first a refinement of the movement step, because the pixel issmaller than the diffraction limit per design, but also subpixel steps,by carefully engineering the ON/OFF individual pixel characteristics.

The natural way to configure direct imaging is to adjust the pixel sizeto the diffraction spot, as in in FIG. 4C. This direct imaging scheme isdescribed for example of a DMD or SLM as for example in (Gauthier,Lenton et al. 2016).

We introduce a new scheme to use Direct imaging of a DMD or SLM, in FIG.4D: we will configure the dimensions of the DMD such that the size of adiffraction limit spot is much smaller—typically 1:5 to 1:11—referred toratio 1:α, of the diffraction size. To create a spot centered on aspecific pixel, positioned at xm, ym, assuming the light addscoherently, we can switch ON all the pixels in a region of size a, orany subregion, contained in it. Any more complex combination of ONpixels, in the region mentioned, will creates spot, almost similar to anAiry, positioned at a predetermined fraction of a pixel, allowing toaddress almost any position on the sample. Even more, departure from thesubregion size, to get even more degrees of freedom, will simplyslightly modify the shape of the spot, with controllable andquantifiable differences, which can be considered in the systemalgorithm.

Such a configuration provides a twofold purpose: on one side it reducesmarkedly the light loss, at the expense of the field of view on theother side we are able to position the point with accuracy better thanthe pixel size.

The configuration described in FIG. 4D, requires high tolerances of thepositioning of adjacent mirrors, in a DMD, or, of the phase of adjacentpixels, in a SLM, to asserts that the different beamlets impinging onadjacent pixels will add coherently and create a single point. However,the actual existing technologies are able to fulfill such requirements.

In this scheme, the spatial bandwidth, in the sense of the size of theregion which can be addressed by the system is traded for a directpositioning of the spot at almost any position, with a simplemathematical recipe.

In the specific case of Biology, the technological development had madesuch a tradeoff practical. Assuming

The diffraction limit to be 200 μmthe availability of a 1920*1024 DMD or SLMα of 7The measured region will span a region of 55*30 μm;this values are adapted to single cells, typically 25-40 μm size.

Additionally, in such a configuration, several independent points can beilluminated simultaneously, and controlled in parallel.

This solution can be improved, as described in FIG. 4E, in order tomitigate the energy loss, on one side, and to be able to move the pointin fraction of the element size on the other side.

Assuming a lower resolution system, based on a galvanometric scanner,FIG. 4a , or preferably on an Acousto-optic deflector, FIG. 4B,multichannel Acousto- or electro-optic deflector, or a wave shaping DMDor SLM, positioned at the pupil of the system, as drawn in FIG. 4E,creating on the DMD or SLM, [48], a point larger than the diffractionlimit. Let assumes that all the pixels are switched off, except a singleone, in a configuration similar to FIG. 4C, not drawn, or a small regionconsisting of a number of adjacent pixels, [51], in a configurationsimilar to FIG. 4D—drawn in FIG. 4E.

The additional intermediate level will simply reduce the energy lossesto roughly the ratio between the size of the two points, the largerpoint created by the first level of point positioning, and thediffraction limited size on the DMD or SLM. Additionally, as in FIG. 4C,and FIG. 4D, several points can be illuminated simultaneously.

The geometry of the system had been described, for simplicity, in thisparagraph, assuming that the scanning device is positioned at theentrance of the system. This configuration is plausible, assuming thatthe beam shaper, obey adequate optical constraints, mainlyTelecentricity. The beam shaper can also be positioned before thescanning device, which will manipulate the distributions directly.Practically this solution may be simpler, but both solutions areadequate and engineering aspects will determine the choice between thetwo configurations.

In another embodiment, of the multiple synchronized points lightdistribution, can be created, using a Wave shaping DMD or SLM,positioned at the pupil of the system in a configuration similar tothose used for example in {Ritsch-Marte, 2009 #39} or similarpublications.

In another embodiment, of the multiple synchronized points lightdistribution, can be created, by a multichannel Acousto- orelectro-optic deflector, as described as a commercial product by thecompany G&H,https://gandh.com/product-categories/multi-channel-modulators-aomc/, asaccessed on Dec. 2, 2020, or by a very fast Acousto- or electro-opticdeflector, to acquire quasi simultaneous points.

Description of Embodiments of the Present Invention: SimplifiedCartesian Algorithms and Control System

We present in FIG. 5, a family of simplified cartesian algorithms andcontrol system for dark tracking and dark addressing.

Assuming a horizontal pattern, represented in FIG. 5A, the position x ofan emitter, materialized by a star on the Figure, relative to thecentral reference line, along the y axis, is directly dependent on theenergy; the theoretical function is, in Conical Diffraction patterns aparabolic dependance, but the actual dependance can be calibrated usinga suitable procedure to take into account small discrepancy. Apotential—small—dependance of the orthogonal directions can also beconsidered by the procedure.

Assuming a vertical pattern, represented in FIG. 5B, the position y ofan emitter, materialized by a star on the Figure, relative to thecentral reference line, along the x axis, is directly dependent on theenergy; the theoretical function is, in Conical Diffraction patterns aparabolic dependance but the actual dependance can be calibrated using asuitable procedure to take into account small discrepancy. Apotential—small—dependance of the energy due to the orthogonaldirections can also be considered by the procedure.

Assuming an axial dependent pattern, described in {Sirat, 2016 #11}represented in FIGS. 5C-5E, the energy is dependent of the position s,the distance in three-dimensions between an emitter and the 3D centralpoint of the distributions. FIGS. 5C-5E represent 3 cuts, Represented asFIG. 5C, FIG. 5D and FIG. 5E at different axial positions, namely, (1)at focus, (2) at an axial position of 0.1 Rayleigh range, and (3) at anaxial position of 0.2 Rayleigh range. At focus, if the point will havebeen at focus AND at the zero of the x-y coordinates, we will havegotten a zero of energy, in this distribution as described in {Sirat,2016 #11} and subsequent patents. The theoretical function is, inConical Diffraction patterns, a parabolic dependance, either of s, or aknown combination of z and r, (FIG. 5F), r being the lateral projecteddistance between the points (r=√{square root over (x²+y²)}). Thecalculation may use the theoretical function or can be calibrated usinga suitable procedure to consider small discrepancy. The dependance ofthe energy due the orthogonal directions must also be considered by theprocedure.

The same procedure can be used with any of the axial dependentdistributions, including all axial dependent distributions described inthe inventions of the inventor, including but not limited to {Sirat,2016 #11; Sirat, 2017 #8; Sirat, 2017 #12; Sirat, 2017 #31; Sirat, 2016#36; Sirat, 2017 #34}, featuring a zero of energy, and other known axialdependent distributions, as known to the Man skilled in Art.

Even if the preferred embodiment is featuring a common zero of thelateral and axial dependent distributions, which simplifies much thealgorithm, as described in FIG. 5, other embodiments can be implementedwith other conditions, with some tolerance on the commonality of thezero of the distributions, with either a penalty in photons cost oreither the need for an additional movement of one distribution relativeto the other(s).

We present in the same FIG. 5, a second simplified cartesian algorithm.

Assuming a first horizontal pattern, represented in Figure FIG. 5G, asan asymmetric version of the pattern described in FIG. 5A, and a secondhorizontal pattern, represented in FIG. 5H, as an asymmetric version ofthe pattern described in FIG. 5A, being a mirror image of the pattern ofFIG. 5G. Both of these patterns can be created using CODIM—ConicalDiffraction Microscopy, by an adequate choice of input and outputpolarisations. The position x of an emitter, materialized by a star,relative to the central reference line, along the y axis, is directlydependent on the sum of the energy collected by the two measurements;the direction of the x position can be measured through the comparisonof the two patterns yielding a measurement value which sign—positive ornegative—depends on the comparison of the two energies. The theoreticalfunction is, in Conical Diffraction patterns a parabolic dependance, butthe actual dependance can be calibrated using a suitable procedure toconsider small discrepancy. A potential—small—dependance of theorthogonal directions can also be considered by the procedure.

Assuming two vertical patterns, FIG. 5I and FIG. 5J, whichbehave—mutatis mutandis—in a way similar to the horizontal patterns.

The patterns FIG. 5A to FIG. 5J (excluding FIG. 5F), symmetrical orasymmetrical, can be created, at an angle (3, chosen to optimize theparameters of the measurement or of the system, instead of horizontal orvertical axis described above.

Any of the measurements created by projecting a sequence of thesepatterns, or combinations thereof, either at the same position of theemitter, measured simultaneously or quasi-simultaneously, or as atime-dependent sequence, or in conjunction to a movement, either imposedby the operator or created naturally, augmented by simple mathematicalprocedures known to the man skilled in art, creates a simpledeterministic lateral, axial or three-dimensional measurement procedure.

These measurements can also be coupled with additional information toyield accurate positioning.

For example, the symmetric pattern measurement is simpler, and in somecases more accurate, in the case that the position polarity is knownfrom external or previous information. Any combination of thesemeasurements, and all of their direct and obvious derivatives can be—andwill be—used in order to maximize the precision, minimize the time, andthe number of photons required for a measurement.

Additionally, a model validation index, imod can be calculated. Thisindex will assert that the measurements are, within a reasonabletolerance, fitting the model defined. It will assert the assumptions ofthe model.

As an example, if the model assumes that the object is a single luminouspoint, the 4 measurements of the second simplified algorithm describedabove, have some predetermined relationship. Departure from thisconstraints will allow detecting outliers, a major issue in manylocalization techniques.

This detection, at the lowest level of information, the raw data is themost reliable way to avoid errors and mistakes.

Moreover, the model validation index can be extended, for example byadding additional measurements, to recognize and quantify additionalcases, as described as metrology above. The recognition process can beeither a predetermined relationship, either from theoretical,experimental or functional grounds, and may even uses Deep learningtechniques as a continuation of {Sirat, 2017 #12}.

Description of Embodiments of the Present Invention: Electronics

In another embodiment, an electronic design, optimized for thisinvention, for all CODIM systems, and for all optical setups usingPockels cell in a set of fixed polarization states, is described.Assuming the use of a single or double Pockels cell to control thepolarization state, one of the limit of practical devices is therequirement to switch from one polarization state to another at highrate. Even if High Voltage Amplifiers and DC to DC voltage sources areavailable commercially, the requirement to switch from one state toanother, for Kilovolt voltages at high speed, requires high currents andexpensive devices. An alternate solution, described in this invention,taking advantage to the fact that a Pockels cell is electrically a lowcapacitance, in the pF range, is to materialize a small number ofvoltage values, by charging relative large capacitors, in the nF orabove range, beforehand, at reasonable current level, and connectingthem when required to the Pockels cell. In an additional andcomplementary embodiment, taking advantage that the Pockels cell is atwo electrodes device and that the voltage creating the optical effectis the difference between the voltage applied on the two electrodes,a—much—lower Voltage Amplifier or DC-to-DC converter is used, either tocompensate for drop in the voltage of the large capacitance or to switchbetween nearby states, as for example the states described in FIG. 5Gand FIG. 5H, or the states described in FIG. 5I and FIG. 5J. Assumingthe voltage on the large capacitance and/or on the Pockels cell ismonitored, using means known to the man skilled in Art, in anotherembodiment, a control system is added to refresh, when required, thevoltage on the large capacitances, taking advantage of the time whenother polarization states are applied to the Pockels.

The references listed below are hereby incorporated herein by reference.

REFERENCES

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I claim:
 1. A method for determining a position in three dimensions of alight-emitting object in a sample, the method comprising: characterizingtwo of the dimensions of the position in a first coordinate system usingan Abbe's loophole technique, by projecting along a first projectionaxis, onto a part of the sample including the light-emitting object, afirst set of distributions of optical radiation having zero intensity ata common center of each of the distributions of the set, measuring theintensity of the light emitted and moving the set of distributions to afirst location on the object wherein the light emissions are at aminimum, such location characterizing such two of the dimensions; andusing an optical module to shape the light emitted from the object,before detecting the light, in a manner wherein a resulting shapedepends on an axial position of the object, recording the shape and theoverall intensity, and using the resulting shape measurement todetermine the axial position.
 2. A method according to claim 1, furthercomprising determining the position of the light-emitting object, witheven higher accuracy, by characterizing all three of the dimensions ofthe position in a second coordinate system using the Abbe's loopholetechnique, by projecting along a second projection axis onto the objecta second set of distributions of optical radiation having zero intensityat the three-dimensional position of each of the distributions of theset, determined according to claim 1, and moving the set ofdistributions to a second location on the object wherein the lightemissions are at a minimum, such second location characterizing allthree dimensions.
 3. A method for determining the position in threedimensions of the light-emitting object according to claim 1 or claim 2,the method further comprising, before characterizing two of thedimensions of the position in the first coordinate system, acquiring arough estimation of the position of two- or three-dimensional positionof the light-emitting object, by standard localization or imagingmethods.
 4. A method for determining the position in three dimensions ofthe light-emitting object, according to any of claim 1 to 3, furthercomprising, in the course of projecting a set distributions selectedfrom the group consisting of the first set and second set ofdistributions and combinations thereof, onto the light-emitting object,measuring the intensity of light emitted along a selected Cartesian axisin a delimited region thereof including a location having minimumintensity, wherein such intensity along such Cartesian axis yields ameasure of the position of the light-emitting object along suchCartesian axis, decorrelated from position of the light-emitting objectalong other axes.
 5. A method according to claim 4, wherein the set ofdistributions includes at least two distributions.
 6. A method fordetermining a position in three dimensions of a light-emitting object,according to claim 4 or claim 5, wherein the set of distributions ofoptical radiation having zero intensity at a common center of each ofthe distributions of the set, is chosen such that the set of valuesmeasured from the intensities and shapes is selected from the groupconsisting of redundant and over determined, in order to providevalidation of the determined position.
 7. A method for determining aposition in two or three dimensions of a set of separated light-emittingobjects, the method comprising: characterizing two or three of thedimensions of the position of each one of the separated light emittingobjects, by projecting, using a scanning device, along a projectionaxis, onto each object of the set of objects, a set of distributions ofoptical radiation having zero intensity at a common center, in two orthree dimensions, of each of the distributions of the set ofdistributions, the center being different for each object of the set ofobjects, measuring the intensity of the light emitted and moving thecenter of set of distributions, by using a scanning device, separatelyfor each object of the set of objects, to a location on the object ofthe set of objects, wherein the light emissions are at a minimum.
 8. Amethod according to claim 7, wherein the scanning device used to movethe positions of the is a SLM or a DMD, positioned at a plane conjugateto the sample, and the scanning device is operating, for a SLM or a DMD,in a mode that either only pixels conjugated to the position of thedetermined positions are in ON mode and the light collected is thedirect path, or, alternatively, in a DMD, only pixels conjugated to theposition of the emitters are in OFF mode and the light collected is theindirect path
 9. A method according to claim 7 or 8, wherein the size ofthe spot corresponding to the diffraction limit is larger than the pixelsize, by a factor between 3 and
 11. 10. A method according to claim 9,in which an algorithm is applied to determine an adequate combination ofpixels ON and OFF, to position the centroid of the spot on the samplewith resolution better than a single, full, pixel of the scanningdevice, projected on the sample plane,
 11. A method according to any ofclaims 7 to 10, wherein a first optical module is used to create a lightdistribution including the emitters position as part of the illuminationdomain
 12. A method according to claims 7 and 11, wherein the scanningmodule is selected from the group consisting of a multichannel acousto-or electro-optic deflector and a Wavefront shaper, and combinationsthereof.